@unpublished{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14412}, year = {1996}, abstract = {Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegen{\"u}ber St{\"o}rungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilit{\"a}t ihres Verhaltens aus.}, language = {de} } @unpublished{VolosevichMeister1998, author = {Volosevich, Alexandra V. and Meister, Claudia-Veronika}, title = {Nonlinear interaction of Farley-Buneman waves}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14851}, year = {1998}, abstract = {The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves' growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated.}, language = {en} } @unpublished{BraunFeudelGuzdar1998, author = {Braun, Robert and Feudel, Fred and Guzdar, Parvez}, title = {The route to chaos for a two-dimensional externally driven flow}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14717}, year = {1998}, abstract = {We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.}, language = {en} } @unpublished{Lukaschewitsch1998, author = {Lukaschewitsch, Michael}, title = {Geoelectrical conductivity problems on unbounded domains}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14704}, year = {1998}, abstract = {This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincar{\´e} inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.}, language = {en} } @unpublished{WittNeimanKurths1997, author = {Witt, Annette and Neiman, Alexander and Kurths, J{\"u}rgen}, title = {Characterizing the dynamics of stochastic bistable systems by measures of complexity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14556}, year = {1997}, abstract = {The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.}, language = {en} } @unpublished{MaassPereverzevRamlauetal.1998, author = {Maaß, Peter and Pereverzev, Sergei V. and Ramlau, Ronny and Solodky, Sergei G.}, title = {An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14739}, year = {1998}, abstract = {The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.}, language = {en} } @unpublished{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14339}, year = {1996}, abstract = {The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived.}, language = {en} } @unpublished{WittKurthsKrauseetal.1994, author = {Witt, Annette and Kurths, J{\"u}rgen and Krause, F. and Fischer, K.}, title = {On the validity of a model for the reversals of the Earth's magnetic field}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13460}, year = {1994}, abstract = {We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.}, language = {en} } @unpublished{KurthsVossWittetal.1994, author = {Kurths, J{\"u}rgen and Voss, A. and Witt, Annette and Saparin, P. and Kleiner, H. J. and Wessel, Niels}, title = {Quantitative analysis of heart rate variability}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13470}, year = {1994}, abstract = {In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.}, language = {en} } @unpublished{ThiessenhusenEspositoKurthsetal.1995, author = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank}, title = {Detection of hidden resonances in Saturn's B-ring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618}, year = {1995}, abstract = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.}, language = {en} } @unpublished{Schmidtmann1995, author = {Schmidtmann, Olaf}, title = {Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13790}, year = {1995}, abstract = {The present paper is related to the problem of approximating the exact solution to the magnetohydrodynamic equations (MHD). The behaviour of a viscous, incompressible and resistive fluid is exemined for a long period of time. Contents: 1 The magnetohydrodynamic equations 2 Notations and precise functional setting of the problem 3 Existence, uniqueness and regularity results 4 Statement and Proof of the main theorem 5 The approximate inertial manifold 6 Summary}, language = {en} } @unpublished{VossKurthsSchwarz1996, author = {Voss, Henning and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Reconstruction of grand minima of solar activity from Delta 14 C data : linear and nonlinear signal analysis}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14083}, year = {1996}, abstract = {Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.}, language = {en} } @unpublished{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14099}, year = {1996}, abstract = {We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.}, language = {en} } @unpublished{MaassRieder1996, author = {Maaß, Peter and Rieder, Andreas}, title = {Wavelet-accelerated Tikhonov-Phillips regularization with applications}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14104}, year = {1996}, abstract = {Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}}, language = {en} } @unpublished{DickenMaass1995, author = {Dicken, Volker and Maaß, Peter}, title = {Wavelet-Galerkin methods for ill-posed problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13890}, year = {1995}, abstract = {Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.}, language = {en} } @unpublished{Jansen1995, author = {Jansen, Wolfgang}, title = {CANDYS/QA : algorithms, programs, and user's manual}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13920}, year = {1995}, abstract = {Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics}, language = {en} } @unpublished{ScherfTian2012, author = {Scherf, Ullrich and Tian, He}, title = {Organic electronics/optics for an energetic life}, series = {Advanced materials}, volume = {24}, journal = {Advanced materials}, number = {5}, publisher = {Wiley-Blackwell}, address = {Malden}, issn = {0935-9648}, doi = {10.1002/adma.201104917}, pages = {576 -- 579}, year = {2012}, language = {en} } @unpublished{FeudelSeehaferGalantietal.1996, author = {Feudel, Fred and Seehafer, Norbert and Galanti, Barak and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14317}, year = {1996}, abstract = {We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.}, language = {en} } @unpublished{BraunFeudelSeehafer1997, author = {Braun, Robert and Feudel, Fred and Seehafer, Norbert}, title = {Bifurcations and chaos in an array of forced vortices}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14564}, year = {1997}, abstract = {We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.}, language = {en} } @unpublished{SeehaferZienickeFeudel1996, author = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred}, title = {Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14328}, year = {1996}, abstract = {We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions.}, language = {en} } @unpublished{SeehaferSchumacher1998, author = {Seehafer, Norbert and Schumacher, J{\"o}rg}, title = {Resistivity profile and instability of the plane sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14686}, year = {1998}, abstract = {The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh-2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.}, language = {en} } @unpublished{ScheelSeehafer1997, author = {Scheel, Stefan and Seehafer, Norbert}, title = {Bifurcation to oscillations in three-dimensional Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14370}, year = {1997}, abstract = {Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.}, language = {en} } @unpublished{RuedigerFeudelSeehafer1998, author = {R{\"u}diger, Sten and Feudel, Fred and Seehafer, Norbert}, title = {Dynamo bifurcations in an array of driven convection-like rolls}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14678}, year = {1998}, abstract = {The bifurcations in a three-dimensional incompressible, electrically conducting fluid with an external forcing of the Roberts type have been studied numerically. The corresponding flow can serve as a model for the convection in the outer core of the Earth and is realized in an ongoing laboratory experiment aimed at demonstrating a dynamo effect. The symmetry group of the problem has been determined and special attention has been paid to symmetry breaking by the bifurcations. The nonmagnetic, steady Roberts flow loses stability to a steady magnetic state, which in turn is subject to secondary bifurcations. The secondary solution branches have been traced until they end up in chaotic states.}, language = {en} } @unpublished{SchmidtmannFeudelSeehafer1997, author = {Schmidtmann, Olaf and Feudel, Fred and Seehafer, Norbert}, title = {Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14431}, year = {1997}, abstract = {The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We desribe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magnetohydrodynamic equations and compare its efficiency with the linear Galerkin approximation. Special bifurcation points, time-averaged values of energy and enstrophy as well as Kaplan-Yorke dimensions are calculated for both schemes in order to estimate the number of modes necessary to correctly describe the behavior of the exact solutions.}, language = {en} } @unpublished{SeehaferSchumacher1997, author = {Seehafer, Norbert and Schumacher, J{\"o}rg}, title = {Squire's theorem for the magnetohydrodynamic sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14628}, year = {1997}, abstract = {The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfv{\´e}n velocity) are raised from small values, two-dimensional perturbations become unstable first.}, language = {en} } @unpublished{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Bifurcation phenomena of the magnetofluid equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13585}, year = {1995}, abstract = {We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.}, language = {en} } @unpublished{FeudelSeehafer1995, author = {Feudel, Fred and Seehafer, Norbert}, title = {Bifurcations and pattern formation in a 2D Navier-Stokes fluid}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13907}, year = {1995}, abstract = {We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).}, language = {en} } @unpublished{FeudelSeehafer1994, author = {Feudel, Fred and Seehafer, Norbert}, title = {On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13390}, year = {1994}, abstract = {We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.}, language = {en} } @unpublished{FeudelSeehaferSchmidtmann1995, author = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf}, title = {Fluid helicity and dynamo bifurcations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13882}, year = {1995}, abstract = {The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.}, language = {en} } @unpublished{Seehafer1995, author = {Seehafer, Norbert}, title = {Nature of the α effect in magnetohydrodynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13919}, year = {1995}, abstract = {It is shown that the ff effect of mean-field magnetohydrodynamics, which consists in the generation of a mean electromotive force along the mean magnetic field by turbulently fluctuating parts of velocity and magnetic field, is equivalent to the simultaneous generation of both turbulent and mean-field magnetic helicities, the generation rates being equal in magnitude and opposite in sign. In the particular case of statistically stationary and homogeneous fluctuations this implies that the ff effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there.}, language = {en} } @unpublished{DemircanScheelSeehafer1999, author = {Demircan, Ayhan and Scheel, Stefan and Seehafer, Norbert}, title = {Heteroclinic behavior in rotating Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14914}, year = {1999}, abstract = {We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.}, language = {en} } @unpublished{SchumacherSeehafer1999, author = {Schumacher, J{\"o}rg and Seehafer, Norbert}, title = {Bifurcation analysis of the plane sheet pinch}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14926}, year = {1999}, abstract = {A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.}, language = {en} } @unpublished{GuastiEngbertKrampeetal.2000, author = {Guasti, Giovanna and Engbert, Ralf and Krampe, Ralf T. and Kurths, J{\"u}rgen}, title = {Phase transitions, complexity, and stationarity in the production of polyrhythms}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14933}, year = {2000}, abstract = {Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook}, language = {en} } @unpublished{HenkelPieplow2014, author = {Henkel, Carsten and Pieplow, Gregor}, title = {Reply to Comment on 'Fully covariant radiation force on a polarizable particle'}, series = {New journal of physics : the open-access journal for physics}, volume = {16}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/16/11/118002}, pages = {8}, year = {2014}, abstract = {We argue that the theories of Volokitin and Persson (2014 New J. Phys. 16 118001), Dedkov and Kyasov (2008 J. Phys.: Condens. Matter 20 354006), and Pieplow and Henkel (2013 New J. Phys. 15 023027) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of the Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is 'diluted' to obtain the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.}, language = {en} } @unpublished{Buerger2014, author = {B{\"u}rger, Gerd}, title = {Comment on "Bias correction, quantile mapping, and downscaling: revisiting the inflation issue"}, series = {Journal of climate}, volume = {27}, journal = {Journal of climate}, number = {4}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0894-8755}, doi = {10.1175/JCLI-D-13-00184.1}, pages = {1819 -- 1820}, year = {2014}, abstract = {In a recent paper, Maraun describes the adverse effects of quantile mapping on downscaling. He argues that when large-scale GCM variables are rescaled directly to small-scale fields or even station data, genuine small-scale covariability is lost and replaced by uniform variability inherited from the larger scales. This leads to a misrepresentation mainly of areal means and long-term trends. This comment acknowledges the former point, although the argument is relatively old, but disagrees with the latter, showing that grid-size long-term trends can be different from local trends. Finally, because it is partly incorrectly addressed, some clarification is added regarding the inflation issue, stressing that neither randomization nor inflation is free of unverified assumptions.}, language = {en} } @unpublished{FoehlischdeGrootOdeliusetal.2014, author = {F{\"o}hlisch, Alexander and de Groot, F. M. F. and Odelius, Michael and Techert, Simone and Wernet, P.}, title = {Comment on "state-dependent electron delocalization dynamics at the solute-solvent interface: soft-x-ray absorption spectroscopy and lambda b initio calculations"}, series = {Physical review letters}, volume = {112}, journal = {Physical review letters}, number = {12}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.112.129302}, pages = {2}, year = {2014}, language = {en} } @unpublished{PikovskijZaksFeudeletal.1995, author = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen}, title = {Singular continuous spectra in dissipative dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787}, year = {1995}, abstract = {We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.}, language = {en} } @unpublished{PikovskijFeudel1994, author = {Pikovskij, Arkadij and Feudel, Ulrike}, title = {Characterizing strange nonchaotic attractors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13405}, year = {1994}, abstract = {Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.}, language = {en} } @unpublished{Pikovskij2015, author = {Pikovskij, Arkadij}, title = {Comment on "Asymptotic Phase for Stochastic Oscillators"}, series = {Physical review letters}, volume = {115}, journal = {Physical review letters}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.115.069401}, pages = {1}, year = {2015}, language = {en} } @unpublished{KurthsPikovskijScheffczyk1994, author = {Kurths, J{\"u}rgen and Pikovskij, Arkadij and Scheffczyk, Christian}, title = {Roughening interfaces in deterministic dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13447}, year = {1994}, abstract = {Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.}, language = {en} } @unpublished{HilczerGerhardScott2014, author = {Hilczer, B{\"o}rn and Gerhard, Reimund and Scott, James F.}, title = {Special Issue of Ferroelectrics in Honor of S. B. Lang}, series = {Ferroelectrics}, volume = {472}, journal = {Ferroelectrics}, number = {1}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0015-0193}, doi = {10.1080/00150193.2014.964099}, pages = {VII -- VIII}, year = {2014}, language = {en} } @unpublished{Gerhard2014, author = {Gerhard, Reimund}, title = {Sidney Lang - his collaboration with the University of Potsdam}, series = {Ferroelectrics}, volume = {472}, journal = {Ferroelectrics}, number = {1}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0015-0193}, doi = {10.1080/00150193.2014.967090}, pages = {5 -- 5}, year = {2014}, language = {en} } @unpublished{AcharyaActisAghajanietal.2013, author = {Acharya, B. S. and Actis, M. and Aghajani, T. and Agnetta, G. and Aguilar, J. and Aharonian, Felix A. and Ajello, M. and Akhperjanian, A. G. and Alcubierre, M. and Aleksic, J. and Alfaro, R. and Aliu, E. and Allafort, A. J. and Allan, D. and Allekotte, I. and Amato, E. and Anderson, J. and Ang{\"u}ner, Ekrem Oǧuzhan and Antonelli, L. A. and Antoranz, P. and Aravantinos, A. and Arlen, T. and Armstrong, T. and Arnaldi, H. and Arrabito, L. and Asano, K. and Ashton, T. and Asorey, H. G. and Awane, Y. and Baba, H. and Babic, A. and Baby, N. and Baehr, J. and Bais, A. and Baixeras, C. and Bajtlik, S. and Balbo, M. and Balis, D. and Balkowski, C. and Bamba, A. and Bandiera, R. and Barber, A. and Barbier, C. and Barcelo, M. and Barnacka, Anna and Barnstedt, J{\"u}rgen and Barres de Almeida, U. and Barrio, J. A. and Basili, A. and Basso, S. and Bastieri, D. and Bauer, C. and Baushev, Anton N. and Becerra Gonzalez, J. and Becherini, Yvonne and Bechtol, K. C. and Tjus, J. Becker and Beckmann, Volker and Bednarek, W. and Behera, B. and Belluso, M. and Benbow, W. and Berdugo, J. and Berger, K. and Bernard, F. and Bernardino, T. and Bernl{\"o}hr, K. and Bhat, N. and Bhattacharyya, S. and Bigongiari, C. and Biland, A. and Billotta, S. and Bird, T. and Birsin, E. and Bissaldi, E. and Biteau, Jonathan and Bitossi, M. and Blake, S. and Blanch Bigas, O. and Blasi, P. and Bobkov, A. A. and Boccone, V. and Boettcher, Markus and Bogacz, L. and Bogart, J. and Bogdan, M. and Boisson, Catherine and Boix Gargallo, J. and Bolmont, J. and Bonanno, G. and Bonardi, A. and Bonev, T. and Bonifacio, P. and Bonnoli, G. and Bordas, Pol and Borgland, A. W. and Borkowski, Janett and Bose, R. and Botner, O. and Bottani, A. and Bouchet, L. and Bourgeat, M. and Boutonnet, C. and Bouvier, A. and Brau-Nogue, S. and Braun, I. and Bretz, T. and Briggs, M. S. and Bringmann, T. and Brook, P. and Brun, Pierre and Brunetti, L. and Buanes, T. and Buckley, J. 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K. and Yamamoto, H. and Yamamoto, T. and Yamazaki, R. and Yanagita, S. and Yebras, J. M. and Yelos, D. and Yoshida, A. and Yoshida, T. and Yoshikoshi, T. and Zabalza, V. and Zacharias, M. and Zajczyk, A. and Zanin, R. and Zdziarski, A. and Zech, Alraune and Zhao, A. and Zhou, X. and Zietara, K. and Ziolkowski, J. and Ziolkowski, P. and Zitelli, V. and Zurbach, C. and Zychowski, P.}, title = {Introducing the CTA concept}, series = {Astroparticle physics}, volume = {43}, journal = {Astroparticle physics}, number = {2}, publisher = {Elsevier}, address = {Amsterdam}, organization = {CTA Consortium}, issn = {0927-6505}, doi = {10.1016/j.astropartphys.2013.01.007}, pages = {3 -- 18}, year = {2013}, abstract = {The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.}, language = {en} } @unpublished{EngbertScheffczykKrampeetal.1997, author = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold}, title = {Tempo-induced transitions in polyrhythmic hand movements}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380}, year = {1997}, abstract = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.}, language = {en} }